Kris Commons and Lewis McGugan also netted for Forest, who kept the Glovers at bay despite Jaime Peters and Andy Kirk scoring to ensure a nervous final few moments.
Forest's success meant despair for Doncaster, who had started the day in second place but must now ride their luck in the end-of-season play-offs.
They lost 2-1 at Cheltenham, and will take on Southend United in the play-offs. Carlisle and Leeds will meet in the other play-off semi-final.
In League Two, Stockport will face Wycombe while Rochdale face Darlington.